Existence of positive solutions to boundary value problems of Caputo fractional difference equations

TL;DR

This paper investigates conditions under which positive solutions exist for boundary value problems involving Caputo fractional difference equations, using Green's functions and fixed point theorems.

Contribution

It provides new sufficient conditions for positive solutions to Caputo fractional difference boundary value problems with non-local boundary conditions.

Findings

Established existence results using Krasnosel'skii fixed point theorem.

Constructed and analyzed Green's function for the boundary value problem.

Identified parameter-dependent conditions for positive solutions.

Abstract

In this paper, we studied the sufficient conditions for the existence of positive solutions to the boundary value problems of Caputo fractional difference equations depending on parameters with non local boundary conditions. We construct and analyse the Green's function to the corresponding boundary value problem and then established the existence results using Krasnosel'skii fixed point theorem.